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We analyze a structure-preserving model order reduction technique for delay and stochastic delay equations based on the balanced truncation method and provide a system theoretic interpretation. Transferring error bounds based on Hankel…

Optimization and Control · Mathematics 2020-08-28 Simon Becker , Lorenz Richter

Traditional projection-based reduced-order modeling approximates the full-order model by projecting it onto a linear subspace. With a fast-decaying Kolmogorov $n$-width of the solution manifold, the resulting reduced-order model (ROM) can…

Numerical Analysis · Mathematics 2026-03-27 Lijie Ji , Sabrina Rashid , Yanlai Chen , Zhu Wang

Linear reduced-order modeling (ROM) is widely used for efficient simulation of deformation dynamics, but its accuracy is often limited by the fixed linearization of the reduced mapping. We propose a new adaptive strategy for linear ROM that…

Graphics · Computer Science 2025-10-01 Yutian Tao , Maurizio Chiaramonte , Pablo Fernandez

We discuss balanced truncation model order reduction for large-scale quadratic-bilinear (QB) systems. Balanced truncation for linear systems mainly involves the computation of the Gramians of the system, namely reachability and…

Optimization and Control · Mathematics 2017-05-02 Peter Benner , Pawan Goyal

A data-driven closure modeling based on proper orthogonal decomposition (POD) temporal modes is used to obtain stable and accurate reduced order models (ROMs) of unsteady compressible flows. Model reduction is obtained via Galerkin and…

Fluid Dynamics · Physics 2021-09-22 Victor Zucatti , William Wolf

Parametric model order reduction by matrix interpolation allows for efficient prediction of the behavior of dynamic systems without requiring knowledge about the underlying parametric dependency. Within this approach, reduced models are…

Dynamical Systems · Mathematics 2025-06-03 Sebastian Resch-Schopper , Romain Rumpler , Gerhard Müller

Piecewise-linear nonlinear systems appear in many engineering disciplines. Prediction of the dynamic behavior of such systems is of great importance from practical and theoretical viewpoint. In this paper, a data-driven model order…

Dynamical Systems · Mathematics 2026-03-19 Akira Saito , Masato Tanaka

This work presents a method for constructing online-efficient reduced models of large-scale systems governed by parametrized nonlinear scalar conservation laws. The solution manifolds induced by transport-dominated problems such as…

Numerical Analysis · Mathematics 2021-01-01 Donsub Rim , Benjamin Peherstorfer , Kyle T. Mandli

Model order reduction algorithms for large-scale descriptor systems are proposed using balanced truncation, in which symmetry or block skew symmetry (reciprocity) and the positive realness of the original transfer matrix are preserved. Two…

Numerical Analysis · Computer Science 2018-11-13 Yuichi Tanji

Although major advances have been achieved over the past decades for the reduction and identification of linear systems, deriving nonlinear low-order models still is a chal- lenging task. In this work, we develop a new data-driven framework…

Fluid Dynamics · Physics 2016-12-26 Jean-Christophe Loiseau , Steven L. Brunton

This work proposes a statistically enhanced framework to address the instability and limited predictive capability of conventional Galerkin-Proper Orthogonal Decomposition (Galerkin-POD) models. The method reformulates the correction of the…

Fluid Dynamics · Physics 2026-04-15 Bijie Yang , Chengyuan Liu , Lu Tian , Yuping Qian , Mingyang Yang

Reduced-order models have been widely adopted in fluid mechanics, particularly in the context of Newtonian fluid flows. These models offer the ability to predict complex dynamics, such as instabilities and oscillations, at a considerably…

Fluid Dynamics · Physics 2023-12-05 Cassio M. Oishi , Alan A. Kaptanoglu , J. Nathan Kutz , Steven L. Brunton

This work presents a scalable control framework based on nonlinear Model Predictive Control for high-dimensional dynamical systems. The proposed approach addresses the key challenges of model scalability and partial observability by…

In this paper, we propose a novel approximation strategy for time-dependent hyperbolic systems of conservation laws for the Euler system of gas dynamics that aims to represent the dynamics of strong interacting discontinuities. The goal of…

Numerical Analysis · Mathematics 2023-01-16 Paola Bacigaluppi , Rémi Abgrall , Svetlana Tokareva

A parametric, hybrid reduced order model approach based on the Proper Orthogonal Decomposition with both Galerkin projection and interpolation based on Radial Basis Functions method is presented. This method is tested against a case of…

Numerical Analysis · Mathematics 2019-12-02 Sokratia Georgaka , Giovanni Stabile , Kelbij Star , Gianluigi Rozza , Michael J Bluck

This article describes a bridge between POD-based model order reduction techniques and the classical Newton/Krylov solvers. This bridge is used to derive an efficient algorithm to correct, "on-the-fly", the reduced order modelling of highly…

Classical Physics · Physics 2011-09-23 Pierre Kerfriden , Pierre Gosselet , Sondipon Adhikari , Stéphane Bordas

This article surveys nonlinear model reduction methods that remain effective in regimes where linear reduced-space approximations are intrinsically inefficient, such as transport-dominated problems with wave-like phenomena and moving…

Numerical Analysis · Mathematics 2026-02-03 Jan S. Hesthaven , Benjamin Peherstorfer , Benjamin Unger

We discuss structure-preserving model order reduction for port-Hamiltonian systems based on an approximation of the full-order state by a linear combination of ansatz functions which depend themselves on the state of the reduced-order…

Numerical Analysis · Mathematics 2023-05-16 Philipp Schulze

This paper introduces a methodology for improving the accuracy and efficiency of reduced order models (ROMs) constructed using the least-squares Petrov-Galerkin (LSPG) projection method through the introduction of preconditioning. Unlike…

Numerical Analysis · Mathematics 2022-03-24 Payton Lindsay , Jeffrey Fike , Irina Tezaur , Kevin Carlberg

We develop a Petrov-Galerkin stabilization method for multiscale convection-diffusion transport systems. Existing stabilization techniques add a limited number of degrees of freedom in the form of bubble functions or a modified diffusion,…

Numerical Analysis · Mathematics 2016-04-20 Victor M. Calo , Eric T. Chung , Yalchin Efendiev , Wing Tat Leung